Risk assessment of human exposure to
Highly Pathogenic Avian Influenza after
vaccination of poultry
Risicobeoordeling van humane blootstelling aan
hoogpathogene aviaire influenza na vaccinatie van pluimvee

Egil Fischer1

1

Giske Lagerweij1
Mart de Jong3

Thomas Hagenaars2

Faculty of Veterinary Medicine, Utrecht University
2
Wageningen Bioveterinary Research
3
Wageningen University
26 september 2023

Project team
Universiteit Utrecht
• Egil A.J. Fischer
• Giske Lagerweij
Wageningen University
• Mart de Jong
Wageningen Bioveterinary Research
• Thomas Hagenaars
• Evelien Germeraad
Rijksinstituut voor Volksgezondheid en Milieu
• Don Klinkenberg

1

Contents
1 Introduction
1.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.2 Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . .

7
8
8
9

2 Within-farm transmission
11
2.1 Short model description . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Results: R and probability of a minor outbreak . . . . . . . . . . 13
2.3 Results: Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.1 No vaccination . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.2 Partial high titre . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.3 Waning immunity . . . . . . . . . . . . . . . . . . . . . . 19
2.3.4 Clinical protection . . . . . . . . . . . . . . . . . . . . . . 25
3 Between-farm transmission
27
3.1 Model description . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2 Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2.1 Passive surveillance . . . . . . . . . . . . . . . . . . . . . 28
3.2.2 Active and passive surveillance . . . . . . . . . . . . . . . 31
4 Conclusions, discussion, and recommendations
33
4.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.3 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Bibliography

36

A Technical description of the models
39
A.1 Overall approach . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
A.2 Within-farm model . . . . . . . . . . . . . . . . . . . . . . . . . . 39
A.2.1 Human exposure . . . . . . . . . . . . . . . . . . . . . . . 42
A.3 Between-farm model . . . . . . . . . . . . . . . . . . . . . . . . . 43
A.4 Parameterization . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

2

Nederlandstalige
samenvatting
Continue circulatie van hoogpathogene vogelgriep (HPAI) in Europese wildevogelpopulaties veroorzaakt introducties van HPAI in pluimvee gedurende het
hele jaar. Aanvullende beschermingsmaatregelen zijn noodzakelijk en vaccinatie
is een veelbelovende oplossing. Vaccinatie kan echter leiden tot verminderde
zichtbaarheid van uitbraken bij pluimvee, waardoor de blootstelling van mensen
aan zoönotische HPAI mogelijk toeneemt.
Hier rapporteren we een risicobeoordeling van menselijke blootstelling gebaseerd op een dynamisch simulatiemodel van HPAI in pluimvee. De beoordeling
is gemaakt met een focus op leghennen en vleeskuikens. Deze modelleringsstudie
bestaat uit een binnenbedrijfs- en een tussenbedrijfsevaluatie. Met het binnenbedrijfsmodel wordt de verandering in blootstelling relatief ten opzichte van de
ongevaccineerde situatie berekend op basis van transmissiesnelheden verkregen
uit vaccinatie-experimenten. Drie scenario’s worden onderzocht: “Partial high
titre”, waarbij slechts een deel van een koppel beschermd is en blijft tegen klinische symptomen èn vooral transmissie ,“Verminderde klinische symptomen”,
waarbij vaccinatie leidt tot bescherming tegen klinische symptomen, maar er
nog wel transmission plaatsvindt en “Waning immunity” waarbij de bescherming tegen transmissie en klinische symptomen door vaccinatie een tijdelijk
karakter heeft. Voor “Waning immunity” is zowel naar een vaccin gebaseerd op
de circulerende stam (homoloog) als een andere stam (heteroloog) gekeken.
Een bestaand tussenbedrijfstransmissiemodel, waarbij infectiekansen zijn gebaseerd op de afstand tussen bedrijven, is aangepast door de tijd tot detectie
en de door vaccinatie verminderde kans op een grote uitbraak uit het binnenbedrijfsmodel te integreren. Voor het tussenbedrijfsmodel hebben we aangenomen
dat alleen bedrijven met leghennen zullen worden gevaccineerd, omdat het huidige vaccin in Nederland in kippen wordt uitgetest en omdat vleeskuikens te
kort leven om voldoende titre op te bouwen.
Resultaten van het binnenbedrijfsmodel geven aan dat er met vaccinatie een
verminderde blootstelling van mensen is in alle scenario’s, behalve in het scenario waarin bijna volledige klinische bescherming optreedt en er geen verandering
is in de transmissie van HPAI binnen pluimveekoppels en tussen pluimvee en
mensen. In de scenarios, waarbij vaccinatie leidt tot verminderde transmissie

3

van HPAIV, kan de detectietijd per bedrijf oplopen, maar de algehele blootstelling van mensen binnen een bedrijf neemt af. Dit komt door een vermindering
van het aantal geı̈nfecteerde kippen op een bedrijf tijdens een uitbraak en een
vermindering van de overdracht naar mensen door besmette gevaccineerde kippen.
Naast de effecten van bescherming tegen verspreiding binnen een bedrijf zal
tussen-bedrijfstransmissie verminderen, doordat de kans op een grote uitbraak
met als resultaat minder geı̈nfecteerde pluimveehouderijen. Hierdoor zal in het
algemeen de blootstelling afnemen. Echter als er klinische bescherming is en
maar 50% van de kippen is beschermd tegen transmissie, zal de blootstelling
van mensen vergelijkbaar zijn met situatie zonder vaccinatie. De maximum
blootstelling is 16 keer groter dan het gemiddelde wat iets groter is dan de
maximale blootstelling in het scenario zonder vaccinatie, waarbij dit 14 keer
groter kan zijn dan gemiddeld. Dus alhoewel het risico iets kan toenemen in dit
uitzonderlijke scenario, dan zal de toename beperkt zijn.
Vaccinatie kan de detectietijd verlengen door verminderde spreiding of verminderde klinische symptomen. Actieve surveillance door ‘bucket sampling’
kan helpen om de detectietijd te verkorten en pluimveehouderijen die anders
niet gedetecteerd worden te detecteren. Dit kan naast de vaccinatie leiden tot
een verdere vermindering van menselijke blootstelling.
In de inschattingen van menselijke blootstelling zijn een aantal onzekerheden.
Hiervoor is de volgende informatie, die deels uit de lopende veldproef zal komen,
nodig.
• Het verloop van de HAR titres in de veldproef kan gebruikt worden om
de risico-analyse up-to-date te brengen.
• Actieve surveillance kan worden ingezet om te monitoren op ongedetecteerde uitbraken. In eerste instantie kan hiermee worden vastgesteld of
silent spread voorkomt in gevaccineerde koppels. Als dit het geval is, kan
er een programma worden ontworpen om besmette bedrijven tijdig te detecteren. Economische berekeningen kunnen met behulp van de resultaten
uit het hier gepresenteerde model worden gedaan om de kosten-effectiviteit
van verschillende surveillance programma’s door te rekenen.

4

Abstract
Continuous circulation of high pathogenic avian influenza virus (HPAIV) in European wild bird populations cause year round incursions of HPAIV in poultry.
Prevention requires additional measures and vaccination is a promising solution.
Vaccination can, however, result in reduced visibility of outbreaks in poultry,
such that the exposure of humans to zoonotic HPAI might increase.
Here we report a risk assessment of human exposure based on a dynamic simulation model of HPAI in poultry. This modelling study exists of a within-farm
and a between-farm part. With the within-farm model the relative change in
exposure is calculated based on transmission rates obtained from vaccination
experiments. Three scenarios are investigated: ‘Partial high titre’, in which a
fraction of birds have a HI-high titre and is protected against clinical signs and
have reduced infectivity if infected ;‘Waning of immunity’, in which birds with
a high H-titre loose their protection after a certain period, and ‘Reduced clinical
signs’ in which all birds (high or low) titre have reduced clinical signs, but only
high titre birds will have reduced infectivity.
An existing between-farm transmission model based on farm distance was adapted to include the time until detection and the reduced chance of major outbreak
from the within-farm model. For the between-farm model we assumed only layer
farms will be vaccinated.
Within-farm model results indicate a reduced exposure of humans with vaccination in all scenarios except for the situation in which almost complete clinical
protection occurs and no change in infectivity of HPAIV within poultry flocks
and between poultry and humans. In other scenarios, where major outbreaks
are possible and detection times might increase, the overall human exposure
decreases due to a reduction of number of infected birds during an outbreak,
reduction of transmission to humans and a reduction of the probability of a
major outbreak. If vaccination only provides clinical protection, but no reduced
transmission in all vaccinated flocks, the risk of a higher human exposure is
present, but within the margins of the current situation.
Based on our model calculations and the assumptions on which it is based,
vaccination is not expected to increase the exposure of humans to HPAIV. Increased detection times do not lead to higher exposure in most scenarios. Even
if the length of exposure is longer due to a reduced infectivity, a lower number of
infected birds and less infected farms results in an overall decrease in exposure.
5

Only under the specific conditions that transmission is not (or hardly) affected and clinical symptoms are absent in vaccinated animals, vaccination might
increase human exposure. Based on transmission experiments, this particular
situation seems unlikely[9, 19], but we have calculated this scenario in case, such
a situation is observed in a field study or from observational data.
Vaccination results in a reduced speed of spread and reduced mortality of high
HI titre birds. This will lead to longer detection times for passive surveillance,
such that weekly active surveillance (bucket sampling) has an added value by reducing the time until detection and detecting otherwise undetected farms. This
will result in less exposure to humans. For unvaccinated farms active surveillance has little added value, because outbreaks are readily detected by passive
surveillance.
To accommodate for uncertainty around the risks of human exposure, the
following recommendation can be made based on this modelling study:
• The HI titres dynamics in a real life circumstances during the entire life
cycle of a flock will be found in the current field experiment. With these
new figures this risk assessment should be updated.
• Active surveillance could monitor the occurrence of undetected outbreaks
and the extend of clinical protection in flocks where the virus can spread.
At first such surveillance can determine whether silent spread does occur,
and if this is indeed the case a program can be designed to detect infected
farms within a reasonable time. The results of the current model can be
used to evaluate the benefit of active surveillance. The costs of such a
program can be calculated to evaluate different surveillance strategies on
feasibility and cost-effectiveness.

6

Chapter 1

Introduction
Since 2003 large epidemic originating from sporadic incursions of high pathogenic
avian influenza (HPAI) have not occurred. Since 2003 risk have been mitigated
by stamping-out, increased bio security, quarantine and movement restrictions.
Since recent year, HPAI is present year round in wild birds in the Netherlands.
This causes the frequent introductions of highly pathogenic avian influenza from
wild birds into poultry farms. The costs (in terms of money and animal lives)
of the eradication of HPAI in poultry are increasing.
Germeraad et al.. 2023 tested four vaccines in an experimental setting against
HPAI H5N1 clade 2.3.4.4b. Vector-vaccines using Herpes virus (HVT) were
found to significantly reduce the reproduction number (R < 1) in an experimental setting. The other two vaccines, one DNA vaccine and one inactivated
virus vaccine, reduce transmission, but were not able to bring the reproduction number under the threshold value (R > 1). The reduction of transmission
was found to be related to the Haemagglutination Inhibition test (HI)-titres [21].
Standardized small-scale vaccination-transmission experiments in a contained
animal facility are an important first step for evaluating the potential effects of
vaccines against HPAI. In a second step, the effect under field circumstances,
as these likely differ from the experimental settings, needs to be investigated
[22, 5]. The protection of vaccination against transmission might also reduce
in time [22, 23, 16, 19]. Although this so-called immune waning has so far
not been reported for vector vaccines against HPAI [9]. Even without immune
waning, due to other factors in the field sub-optimal vaccination could occur.
Sub-optimal vaccination might lead to silent spread of the infection, when clinical symptoms remain reduced in vaccinated birds. This has been predicted [20]
and observed previously [15, 18].
Silent spread of the infection might prolong the time during which humans (in
particular those working with poultry) are exposed to HPAI. HPAI is a potentially zoonotic infection [14] and a prolonged exposure increases the likelihood
of an infection occurring. On the other hand, successful vaccination of a part
of the flock increases the probability that the the introduction of the virus will
7

only lead to a minor outbreak [7]. Vaccinated birds were producing fewer virus
particles [9], which is reflected in a decreased transmission towards birds and
thus most likely to humans [12, 6]. It is thus not straightforward how these
factors balance out and whether vaccination will increase or decrease human
exposure.
Commissioned by the ministry of Agriculture, Nature and Food quality we
conducted a risk assessment for the exposure of humans to HPAI when poultry
is preventively vaccinated against avian influenza. The study uses an infectious
disease simulation model based on the results of Germeraad et al. 2023 and
extrapolates these to poultry farms in the Netherlands taking into account the
possibility of sub-optimal vaccination.

1.1

Objectives

The aim of this study is to determine the change in human exposure to potentially zoonotic high pathogenic avian influenza under a vaccination strategy of
poultry.
The exposure to HPAI is calculated cumulatively over a simulated outbreak
in different scenarios and divided to the average cumulative exposure in a scenario without vaccination. This ratio will give an indication of an increased or
decreased risk of exposure.
Exposure is calculated
1. based on an outbreak on a single farm
2. based on an epidemic of multiple farms
The simulations of outbreaks on a single farm gives more detailed insight in
the risk of vaccination for human exposure in a single infected farms and the
effect of factors, such as the size of the farm. Simulations over multiple farms
investigate the effect of vaccination on human exposure on the national level.

1.1.1

Approach

This is a modelling study in which the knowledge on HPAI transmission and
effect of vaccines is described in two mathematical models; one for an outbreak
in a single farm and one for an epidemic among farms. The parameters of the
models are obtained from literature and a report by WBVR, Utrecht University,
Wageningen University and RoyalGD [9] (see Table 2.1). The first within-farm
model used to calculate the probability of a minor outbreak within-farm, time
until detection of farms, and human exposure to HPAI in a single farm. We used
a stochastic event-based Susceptible-Infected-Recovered (SIR) model with two
types of birds. Birds either with high titre due to vaccination, which reduces

8

the infectivity (rate of infecting other birds), lengthens the infectious period and
protects against clinical signs. Birds with a low titre are assumed to have the
same characteristics as unvaccinated birds.
Human exposure in the within-farm model is calculated based on the epidemic
curve. Assuming that the rate of transmission from bird-to-human is proportional to bird-to-bird transmission. The absolute probability of infection depends on many more factors, such as being an employee or not, number of visits
to a flock, compliance with bio-security measures, ventilation and the doseresponse. Therefore, we could not calculate the absolute probability of infection
with any accuracy. We determined the relative risk of vaccination on the exposure to HPAI by calculation of the total exposure during an outbreak (until
detection) and dividing this by the mean exposure during an outbreak without
vaccination.
The second between-farm model is an individual-based stochastic simulation
model in which a farm is the epidemiological unit. The individual characteristics of a farm are size, type of farm, vaccination status and time until detection.
Time until detection and human exposure are derived from the within-farm
model. The human exposure of all infected farms is added and divided by the
mean total human exposure in a scenario without vaccination.
Technical details of the model and methods are described in Appendix A.
Short descriptions of the methods are included in separate sections within the
results.

1.1.2

Scenarios

The effect of vaccination is compared to a baseline without vaccination. In the
baseline, we assumed no vaccination and a 99% mortality of infected birds. Outbreaks were simulated for several scenarios (see Table 1.1).In all scenarios, birds
with a high HI-titre will have clinical protection against severe disease and mortality, and will not be observed as being infected unless they die of other causes.
The scenarios were ‘Partial high titre’, in which only a part of the population
has a high HI-titre, ‘Waning of immunity’, in which the high HI-titre lasts for
a specific period depending on the strain being heterologous or homologous to
the circulating strain and ‘Clinical protection’ in which low titre birds are partially protected against clinical symptoms. Within each scenario we simulated
outbreaks for several parameter settings (Table 1.1). The simulated outbreaks
are used to determine the time of detection by either passive surveillance, when
a threshold of death birds is reached, or by active surveillance, when active
monitoring of dead birds is implemented.

9

Scenario

Values

Partial high titre without immune waning
Percentage high HI-titre phigh

50% − 90%

Immune waning scenarios
Immune waning a
Thl
Mean(days):
Std.dev.(days):
Moment of introductionb t0

Homologous Heterologous
514
280
86
140
0,50, 100,200,300,400,500

Reduced clinical signs
Percentage high HI-titre
Probability of dying
after infectious period a

phigh

0%, 50%

ϕl
ϕh

0.50
0.01

Reference

[9]

Estimated from
[19]

Table 1.1: Parameter values for the scenarios.
a
Subscripts h = high titre, l = low titre
b
The moment of introduction t0 and the waning rate νhl determine the initial
percentage with a high HI titre: e−νhl t0

10

[9]

Chapter 2

Within-farm transmission
2.1

Short model description

A detailed description including parameterization of the model can be found in
the appendix A.
Infection dynamics The within-farm model divides the population into two
groups (high titre and low titre). High titre birds are expected to have the same
susceptibility as low titre birds, but differ in the infectivity [21]. Whether a bird
has a high or low titre birds can be due to biological factors (e.g. physiological
differences between chickens), environmental factors (e.g. prior exposure to
avian influenza), or human factors (e.g. incorrect application of the vaccine).
In our model, the birds are randomly divided into high or low titre. In the
scenarios with immune waning, high titre birds can become low titre birds.
High titre birds can become infected and due to the vaccination will have a
longer infectious period because these will not die. The infectious period of
high titre birds is 4.0 days versus 3.0 days of low titre birds. At the end of the
infectious period birds either die in 99% of the cases for low titre birds and 1%
of the high titre birds. Birds that do not die will be considered immune. Low
titre birds will transmit the infection with the same rate as non vaccinated birds
and we used the value of 1.13 day −1 from the study by Germeraad et al.2023.
For the high titre birds we used the value of 0.058 day −1 from Table 2 in Sitaras
et al.2016. This choice was made, because no transmission was measured in the
first study for high titre birds.

11

12
ϕl
ϕh
νhl

10
0.0005 day− 1
1.31 day−1
0.058 day−1
1.31 day−1
0.058 day−1
3.0 day
(αl = 60, ρl = 20)
4.0 day
αh = 80, ρh = 20
0.99
0.001
0.0 day−1

20 000 - 73 000

38 000
42 days
32 000
510 days
15 000 - 64 000

Range

Value

[9, 13]

[9]
[21]
[9]
[21]
[9, 13]

Reference

Table 2.1: Parameters and initial values. l = low titre, h = high titre, α is shape parameter of a gamma distribution and ρ
the rate parameter

Immune waning

Dying after infectious period

αh /ρh

Parameter
Symbol
Flock size and production round
Flock size broilers
N
Duration production cycle broilers
Flock size layers
N
Duration production cycle layers
Infectious, vaccination and mortality
Initial infected birds
I0
Background mortality rate
µ
Intra-type transmission coefficient
βll
βhh
Inter-type transmission coefficient
βlh
βhl
Mean infectious period
αl /ρl

Detection Detection is modelled by passive surveillance when the mortality
on a farm is more than 0.5% of the flock during two consecutive days1 . Alternatively, we studied the effect of active surveillance assuming that all birds
dying during a 7-day interval are tested at the end of that interval. The time of
the first test is assigned randomly between 0 days and 7 days since the start of
the simulation. In the active surveillance scenario we simulate testing of pooled
samples of carcasses collected for destruction (bucket sampling).
Parameter
passive surveillance
Detection threshold
Detection time frame
active surveillance
Time interval
Probability farm in active surveillance
Probability dead animal in active surveillance
Test sensitivity per animal

Value

Reference

0.5% of flock
2 days

1

7 days
1.0
1.0
0.99

[9]

Table 2.2: Parameters for detection module

Human exposure The main objective of this study is a comparison of the
risk of human exposure when poultry is vaccinated with the current situation
without vaccination. Human exposure is calculated as the cumulative force-ofinfection during the whole period of an outbreak. The outbreak ends either at
detection, or when the outbreak fades out before detection. The cumulative
force-of-infection is divided by the cumulative force-of-infection of the baseline
scenario to obtain a relative risk of exposure due to an outbreak. We do not
calculate absolute values, because the actual exposure is determined by many
unknown parameters, such as the amount of virus particles inhaled, the exact
dose-response and the time during which air with virus particles is inhaled.

2.2

Results: R and probability of a minor outbreak

The stochastic model for within-farm transmission is used to calculate the probability of a minor outbreak2 given that the infection is introduced on a farm.
The probability of a minor outbreak after introduction does not depend on the
size of the farm, because in the first phase of an outbreak the number of birds
will not be limiting. Therefore, these results are applicable to all farm sizes.
1 https://www.nvwa.nl/onderwerpen/vogelgriep-preventie-en-bestrijding/vraag-enantwoord/mijn-vogels-hebben-vogelgriep.-waar-moet-ik-dit-melden
2 A minor outbreak is defined as an outbreak that goes extinct by chance in a early stage
of the outbreak, rather than fading out due to a lack of susceptible animals.

13

First the relationship between high titre and the probability of a minor outbreak is calculated assuming that 10 birds will initially be infected either all
with a high titre, all with a low titre or that these are equally distributed over
the high titre and low titre.
At around 75% of the population having a high titre against the introduced
strain, the population is protected against a major outbreak (R < 1), which is
the same as reported in Germeraad et al.. 2023. Here we also calculated the
probability of a minor outbreak for sub optimal protection, when not all birds
have a high titre. The probability of a minor outbreak is negligible, when less
than 50% of the birds has a high titre. Between 50 % and 75 % high titres, the
probability of a minor outbreak rapidly increases (Figure 2.1).

Figure 2.1: Probability of a minor outbreak in relation to R the proportion of
birds with a high titre and initial infections occurring either all in high, all in
low or proportionally distributed over high and low titre groups.
The calculation of the probability of a minor outbreak is used further on
in the between-farm simulations. The probability of a major outbreak is used
to determine if a farm will or will not experience an outbreak at introduction
(Chapter 3). Technically we reduced the transmission rate between two farms
by the probability of a major outbreak on that farm.
14

2.3

Results: Scenarios

2.3.1

No vaccination

The scenario without vaccination is used to investigate the effect of length of
production cycle (layer vs. broiler) and the size of farms on the infection dynamics and the detection time. We used the sizes of 25% percentile, median,
and 75% percentile of Dutch Layer and Broiler farms. In the further scenarios,
broilers were no longer used as we assume that only layers will be vaccinated.
Outbreaks
Without vaccination introduction leads to an outbreak in all simulations with
small fractions of susceptible and recovered animals at the end of the simulation
(Figure 2.2). The outbreak peaks just around 10 days post introduction. This
is similar for all farm sizes.

Figure 2.2: Baseline with no vaccination. Layer starts with 15 000, 32 000 or
64 000 birds, Broiler with 20 000, 38 000 or 73 000. Layers live for 510 days and
Broilers for 46 days. S = susceptible, I = infectious, R = recovered.

Detection
In the scenarios without vaccination, the detection time for passive surveillance
in layer and broiler is expected between 8 - 9 days after introduction (Figure 2.3),
15

which is similar to values estimated for outbreaks in the Netherlands previously
[13]. The size of the flocks does not affect the time until detection, because the
exponentially growing number of dead birds is not limited for the sizes of farms
that we are interested in.
Active surveillance based on weekly sampling of dead birds is not likely to
improve the detection time. With a 7 day interval of testing, the first sample
will be between 0 to 7 days after the introduction of the disease, and on average
birds will die 3 days after infection. The expected detection time is thus between
3 and 10 days, which is similar to the passive surveillance. Active surveillance
will, however, always be accompanied by passive surveillance. Therefore, we
also determined the earliest (minimum) detection time for each run. This is the
time at which in the farm is detected by either the passive or active surveillance.
The mean detection time does decrease in this scenario (Figure 2.3 .

Figure 2.3: Detection times for passive (gray) and active (orange) surveillance
and the minimum of these times(red) for the baseline scenarios.Each row represents a farms size as indicated on the right panel descriptions. The left three
columns show broiler farms and the right three layer farms.
For broilers the probability of slaughter before detection is substantial due
to the short production cycle.

2.3.2

Partial high titre

We studied the effect of Partial high titre, where due to a variety of causes
not all chickens might obtain a high HI titre. We studied populations in which
50% to 90% of chickens have high HI titres and compared this to a population
16

without vaccination.
Outbreaks No major outbreaks should occur above 75% high titre birds (section 2.2 Figure 2.1). In our simulations, we see indeed no major outbreaks for
values above this threshold (i.e. simulations with 80% or 90% high titre birds)
Major outbreaks occur in 100% of the simulations, when the percentage of high
titre birds is less than 75%. In these simulation, 95% of the low titre birds
become infected and also a proportion of the high titre birds. (Figure 2.4).

Figure 2.4: Infection dynamics for median size layer farm (32,000) with different fractions of birds with high titre. Each row are scenarios with a specific
percentage of birds with a high titre as indicated in the panel labels at the right
side.
I = infectious, R = recovered, 1 = low titre, 2= high titre.

Detection Detection times for passive surveillance (Figure 2.5) are not very
sensitive to farm sizes although they might differ a few days between small
(15,000 birds) and large farms (64,000 birds). Partial high titre will increase
detection times for passive surveillance dramatically. For simulations with 70%
high titre birds the threshold of 0.5% dead birds in two consecutive days will
not be reached. For farms with more than 75% high titre, only minor outbreaks
occur that will not be detected by passive surveillance.
Combined passive and active surveillance will always pick up the infection.
The high sensitivity per animal to be detected, will result in detection of one of
the original ten infected birds. The probability that these will not be detected
is (1 − 0.99)10 = 10−21 ≈ 0. The detection time for the simulations with 0%,
50% or 60% high titre birds is equal or longer than passive surveillance due to
17

the sampling frequency of 7 days in the unvaccinated populations(Figure 2.5) .

Figure 2.5: Partial high titre: Detection times different layer farms size (15 000
= 25% percentile, 32,000 = median and 64,000 is 75% percentile of Dutch farms)
and different fractions of birds with high titres. I = infectious, R = recovered,
1 = low titre, 2= high titre.

Human exposure The longer detection times for passive surveillance in imperfectly vaccinated flocks will not lead to a higher exposure of humans (Figure
2.6). The explanation for this result is under this scenario the size of outbreak is
smaller (fewer infected birds) than without vaccination. Additionally we assume
that the exposure by high titre birds is proportional to the transmission rate,
which is more than 20 times lower, while the duration of exposure by a single
bird is on average 1 day longer (infectious period of 4 instead of 3 days). These
assumptions are challenged in the scenarios with clinical protection (Section
2.3.4).

18

Figure 2.6: Partial high titre: Human exposure for an outbreak one farm relative
to mean exposure without vaccination from introduction until either passive
surveillance or fade-out of infection for different layer farms size (15 000 = 25%
percentile, 32,000 = median and 64,000 is 75% percentile of Dutch farms) and
different fractions of birds with high titres. Active is detection time by active
surveillance only, Passive is detection time for passive surveillance only, and
Minimum is the shortest detection time of either. I = infectious, R = recovered,
1 = low titre, 2= high titre.

2.3.3

Waning immunity

In this scenario we investigate waning of immunity in layers, when the vaccine
is homologous or heterologous to the circulating HPAI strain. We consider
introduction at 0, 50, 100, 200, 300, 400 or 500 days after protection has build.
In reality it will take some weeks before vaccination can start and to build up a
titre.
Homologous strain The animals have a gamma-distributed period between
having a high titre, becoming low titre with average of 514 days (73 weeks) and
a standard deviation of 85 days (12 weeks) [19] (see Appendix A.4and Figure
A.1) . We consider the case when the infection is introduced 0, 50, 100, 200,
300, 400 or 500 days after (partial) protection of the vaccination occurs, which
corresponds in this scenario to an initial fraction of high HI titre birds of 100.0%,
100.0% 100.0%, 99.9%, 99.8%, 91.8% and 54.5%.

19

Heterologous strain The animals have a gamma-distributed period between
having a high titre, becoming low titre with average of 280 days (40 weeks) and
a standard deviation of 140 days (20 weeks). Only 70% of the animals will
build up a high titre for the circulating strain [19] (see Appendix A.4and Figure
A.1). We consider the case when the infection is introduced 0, 50, 100, 200,
300, 400 or 500 days after (partial) protection of the vaccination occurs, which
corresponds in this scenario to an initial fraction of high HI titre birds of 70.0%,
69.6%, 66.0%, 47.5%, 26.6% and 12.5% and 5.2%.
Outbreaks When introduced before 400 days after vaccination with a homologous strain, the percentage of birds with low titre is still below the threshold
of a major outbreak and thus all outbreaks will be minor (Figure 2.7a). The
minor outbreaks can be slightly bigger than in the scenario without waning of
infection, although at the moment of introduction the same fraction of high HI
titre occurs. Also waning of immunity can extend the length of an outbreak before fade-out occurs. When the threshold is passed, a major outbreak will occur
similar to the ‘Partial high titre’ scenarios (see section 2.3.2). When a heterologous strain is circulating, all introduction times will result in a major outbreaks.
The size of the outbreaks depends on the time of introduction (Figure 2.7b).
Detection
Introduction at time 0 after vaccination (this is the moment that vaccination
is fully effective) with a homologous strain until 400 days after vaccination, the
minor outbreaks will not be detected even if active surveillance is implemented.
The number of infected birds that die will be too low for detection. This is
because of almost 100% high titre bird, which differs from the ‘Partial high
titre’ scenario for which the highest coverage still had 10% with a low titre.
Introductions 500 days will be detected, but for minor outbreaks only by active
surveillance. Introduction at 500 days after vaccination will result in major
outbreaks that will be detected by passive surveillance on average 10.5 days
after introduction, which is later than the baseline scenario of 8.4 days.
When a heterologous strain is circulating, passive detection is not able to
pick up the infection. Although a large number of birds do get infected (Figure
2.8b), the percentage of dead birds remains below 0.5% per day for any two
consecutive days (in this case 160 dead birds per day).
Human exposure
Human exposure will be lower than without vaccination even when the vaccine protection wanes in time. This will be the case for both the situation in
which a homologous strain (Figure 2.9a) or a heterologous strain (Figure 2.9b)
is circulating.
Similar to the scenario “Partial high titre”, either a minor outbreak occurs or
when a major outbreak is possible the detection times are close to the baseline,

20

(a) Homologous strain

(b) Heterologous strain

Figure 2.7: Infection dynamics with waning immunity in a median size layer
farm (32,000), when high HI titres wane and the infection is introduced at day
0, 50, 100, 200, 300, 4000 or 500 days after vaccination. I = infectious, R =
recovered, 1 = low titre, 2= high titre.

21

(a) Homologous strain..

(b) Heterologous strain.

Figure 2.8: Immune waning: Detection times median sized layer farm (32,000)
and different introduction times (right panel labels). If no bars are plotted, the
introduction will not be detected. Active is detection time by active surveillance
only, Passive is detection time for passive surveillance only, and Minimum is the
shortest detection time of either. I = infectious, R = recovered, 1 = low titre,
2= high titre.

22

while the exposure to humans is reduced due to a smaller number of infected
birds and reduction of transmission in high HI titre birds.

23

(a) Homologous strain.

(b) Heterologous strain.

Figure 2.9: Immune waning: Human exposure relative to that of the median
human exposure in the baseline for a median sized layer farm (32,000) and
different introduction times (right panel labels). For those simulations in which
no detection takes place the exposure until fade-out of the outbreak are used.
Active is detection time by active surveillance only, Passive is detection time for
passive surveillance only, and Minimum is the shortest detection time of either.
24

2.3.4

Clinical protection

We investigated the effect on human exposure, when vaccination protects against
clinical symptoms by reducing the mortality at the end of the infectious period
for birds both with a high or a low titre. The clinical protection for low titre
birds was modeled as 0.1% or 50% mortality at the end of the infectious period.
High titre birds will have a mortality rate of 0.1% in all scenarios. Simulations
were done for 0% and 50% high titre birds meaning that the transmission rate
was reduced for either none or 50% of the animals (Table 1.1).
Detection
If the vaccination will not protect against transmission, but does protect against
clinical disease, the detection times for passive surveillance will increase substantially (Figure 2.10. When only 0.1% of birds die of the infection, passive
surveillance is no longer able to detect an outbreak. If only 50% of the birds
are protected against death, but all transmit at the same rate as unvaccinated
birds, the detection times for passive surveillance increase with only one or two
days on average compared to the baseline scenario.
Active surveillance will effectively find the first dead infectious birds even
when almost no birds will show clinical signs or have excess mortality. This is
due to infected birds dying with the same background mortality as non-infected
birds and are thus sampled, and the assumed high sensitivity of active sampling.

Figure 2.10: Clinical protection: Detection times for surveillance for the scenarios with clinical protection. Active is detection time by active surveillance
only, Passive is detection time for passive surveillance only, and Minimum is
the shortest detection time of either. When no bars are shown, none of the
simulated outbreaks was detected by this surveillance method.

25

Human exposure
The longer detection times for passive surveillance in clinical protected flocks
can lead to a higher exposure of humans (Figure 2.11). In both scenarios where
transmission is not affected by vaccination, the exposure will increase with 50%
to 300%. Especially when clinical protection is high (0.1% deaths), but no
effect on transmission occurs the exposure can be very high. Active surveillance
can mitigate this but not in all cases. If no clinical symptoms are present in
50% of the birds and no reduction of transmission occurs the overall exposure
will be only slightly higher. When 50% of the flock has a high titre that will
reduce transmission and the low titre birds have a 50% chance of dying (a more
likely scenario [9]), the human exposure will be lower than that in the baseline
scenario.

Figure 2.11: Clinical protection: Human exposure of an outbreak until detection relative to mean exposure without vaccination for the clinical protection
scenarios. Percentage high titre indicates scenarios with reduced transmission.
Active is detection time by active surveillance only, Passive is detection time for
passive surveillance only, and Minimum is the shortest detection time of either.

26

Chapter 3

Between-farm transmission
3.1

Model description

Between-farm transmission was modelled assuming that the transmission between farms depends on the distance rij between farms (Eq. 3.1 ). This is a
well established method of modelling the transmission dynamics between farms
[3, 1, 2]. We used the parameterization by Boender et al. 2007.

h(rij ) =

h0
 α
rij
1+
r0

(3.1)

We adapted the code by Beninca et al. 2020 to accommodate for vaccination. Vaccination was modelled by a reduced susceptibility of vaccinated farms.
The susceptibility was equal to the probability of a major outbreak given a
certain amount of high titre animals. We considered vaccination of layers and
no vaccination of broilers, ducks or turkey. For each infected farm the total
human exposure is randomly drawn from the within-farm simulations based on
vaccination status.
Detection and human exposure
Based on the vaccination status of infected farms we drew a random detection
and human exposure value from the outcomes of the within-farm model (e.g.
Parameter
h0
α
r0

description
Infection rate at distance 0
Kernel shape
Spatial scaling

value
0.002 day−1
2.1
1.9 km

Table 3.1: Parameters of the spatial kernel [4]
27

Figure 2.3 for detection). We report the ratio between the exposure summed
over all infected farms in the baseline and the vaccination scenarios. In this part
of the report we will thus increase the scope from the effects on a single farm
to the national level.

3.2

Scenarios

To assess the risk we formulate a few possible scenarios based on the withinfarm simulations. In the ’Partial high titre ’ scenario we consider that 50% of
the birds are protected against clinical signs and no effect of transmission. In
this scenario major outbreaks are possible, the detection times were longer, but
the exposure of an outbreak on a single farm was less. The second scenario is
‘Waning of immunity’ in this scenario the immunity wanes after on average 514
days (for a homologous strain) or 280 days (for a heterologous strain) rendering
the farm partially protected against a major outbreak. The amount of waning
is determined by drawing random times since vaccination between 0 and 540
days for the flocks. The last scenario is ‘Clinical protection’ in which we assume
again 50% protection against death, but not protection against transmission.
We studied both introduction in Densely populated poultry areas (DPPA) and
in sparsely populated poultry areas (SPPA). For each farm we calculated the
density of farms within 1 km of that farm (i.e. the point density). For DPPA
areas we selected from the 5% farms with the highest point density and for
SPPA we selected from the 25% farms with the lowest point density.

3.2.1

Passive surveillance

Number of infected and culled farms
The effect of vaccination is largest in the immune waning scenario with a homologous strain (Figure 3.1). In this scenario, a vaccinated farm is protected
against a major outbreak up to 400 days due to almost 100% high titre birds.
Therefore, the majority of farms will have protection against a major outbreak
resulting in just a few runs with additional infected farms. Please note that the
scenario without waning assume that only 50% of a flock has a reduced transmission due to a high titre, the number of infected farms will decrease. Clinical
protection will slightly increase the chance of major outbreaks with in one run
even almost 40 infected farms.
Human exposure
The variation of human exposure without vaccination ranges in our simulations
between 0.01 and 10 times the mean exposure. When clinical protection occurs
together with 50% birds with reduced transmission the exposure will increase
to a range of 1 to 100 times the mean exposure. Reduced transmission will
decrease the mean exposure and the range is narrower. Waning immunity causes
a distinct difference between small outbreaks in farms with partially high titre
28

(a) Densely Populated Poultry Area

(b) Sparsely Populated Poultry Area

Figure 3.1: Histogram of number of infected farms for an epidemic starting in
a high density poultry area or a low density poultry area.
but very low exposure, and larger outbreaks with multiple infected farms with
on the same mean exposure as in the unvaccinated case.
When the infection starts in SPPA the outbreaks in terms of number of
farms will be smaller and the human exposure will also be smaller. The clinical
protection and waning protection scenarios have a few larger outbreaks due to

29

(a) Densely Populated Poultry Area

(b) Sparsely Populated Poultry Area

Figure 3.2: Exposure as sum of all infected farms in an epidemic relative to
baseline scenario in the same area.
undetected infected farms. Comparing outbreaks starting in an SPPA, the ratio
of exposure between the baseline without vaccination and the other scenarios is
similar to that of the DPPA (see Figure 3.2).

30

Figure 3.3: Histogram of number of infected farms for an epidemic starting in
a high density poultry area and in which active and passive surveillance occur.

3.2.2

Active and passive surveillance

Number of infected and culled farms
The combination of active and passive surveillance changes the number of infected farms from the scenario with only passive surveillance towards less infected farms (Figure 3.3).
Human exposure
Active surveillance added to passive surveillance decreases the risk of outbreaks
with higher human exposure than in the median of baseline outbreaks 3.4. Especially for the scenario with clinical protection, the human exposure is less
when active surveillance is added to passive surveillance.

31

Figure 3.4: Exposure as sum of all infected farms in an outbreak with active and
passive surveillance relative to baseline scenario with only passive surveillance

32

Chapter 4

Conclusions, discussion, and
recommendations
4.1

Conclusions

Based on our model calculations, vaccination is not expected to increase the
exposure of humans to HPAIV. Increased detection times do not lead to higher
exposure in most scenarios, because an outbreak in a farm has a lower number
of infected birds and there is reduced transmission from birds-to-humans reduce
exposure. Also less farms will be infected given vaccination due to a smaller
probability of a major outbreak, further reducing exposure on a national level.
Only under the specific conditions that transmission is not (or hardly) reduced
and clinical symptoms are absent in vaccinated animals, vaccination might increase human exposure. This particular situation seems unlikely for (vector)
vaccines [9], but cannot be excluded such that monitoring is required.
Vaccination results in a reduced speed of spread and reduced mortality of
high HI titre birds resulting in longer detection times for passive surveillance,
such that weekly active surveillance (bucket sampling) has an added value by
reducing the time until detection and detecting otherwise undetected farms.
This will result in less exposure to humans. For unvaccinated farms active
surveillance implemented as weekly bucket sampling will have some but limited
added value, because outbreaks are readily detected by passive surveillance.
More frequent bucket sampling can reduce the detection time as was shown
previously [11].

4.2

Discussion

This report uses a simulation model to investigate the risk of a situation that is
not present in reality. This means that the results are a structured summary of
current knowledge and certain simplifications were required to keep the model

33

tractable and outcomes interpretable. An important assumption underlying
our calculations is that the human exposure can readily be calculated from the
exposure to birds accumulated over time. We refrained from calculating an
absolute probability of infection of humans (e.g. 10% versus 20% chance of
contracting the infection during an outbreak). To do this one would at first
require a dose-response of avian influenza to humans. Such studies have been
conducted for human adapted influenza viruses [6, 12], but this cannot directly
be translated to poultry adapted strains. Secondly, this would require a proper
quantification of the number of virus particles a human is exposed to in an
outbreak. This varies between different people, stables, weather conditions etc.
Therefore, this is unfeasible and for the purpose of this study not necessary.
Our outcome quantifies the cumulative exposure towards humans in a more
abstract way. The question is not how much vaccination will change the risk
of humans, but if it will increase or decrease compared to the situation without vaccination. Therefore, we report the ratio of exposure of humans between
the scenario with and without vaccination. This ratio cannot directly be interpreted as a relative risk (ratio between probability of being infected for the
vaccinated scenarios and unvaccinated scenarios). If the exposure is low and the
probability of infection increases (almost) linearly with exposure, the ratio between exposure will be close to the relative risk, but if exposure is high and the
probability of infection approximates 1 in both the scenarios with and without
vaccination the relative risk is 1. Therefore, the actual relative risk is between
the reported ratio and 1. In this study we therefore present visualisations rather
than numbers, because the interest lies in a qualitative result, whether vaccination increases or decreases the risk of human infections.
Four assumptions in the between-farm model might influence results on the
effectiveness of vaccination. The first assumption is that vaccines are protective
from the moment of the start of a production cycle. This will overestimate the
effectiveness of vaccines. This is a simplification of the reality, that effects the
total number of infected farms in the simulations. The second assumption is
that farms with a minor outbreak do not contribute to exposure to humans.
This will slightly underestimate the exposure in simulations with vaccination,
but the impact is negligible due to the short infectious period and extremely
low number of infected birds. Thirdly, we have also assumed that all layers
receive the vaccine. There is no differentiation between farms or birds. This
might overestimate the effect of vaccination, but will not increase the exposure
of humans above that of a situation without vaccination. Lastly, we assume
infection dynamics and related detection times to be similar for layers, broilers,
ducks and turkey. Silent spread among other types and species of poultry than
layer might occur [10]. Again this will not affect the conclusion in an change of
risk between a situation with or without vaccination in a qualitative way. The
only concern would be when new variants are able to evolve, but that is outside
the scope of this assessment.
Clinical protection might increase human exposure due to the handling of
34

infected birds. Although professionals in the poultry sector are aware of the
zoonotic potential of HPAIV, absence of clinical symptoms could lead to more
contact between humans and infected birds, if these birds are not recognized as
being infected. The risk for humans could then increase when the vaccines are
protecting against clinical symptoms but not or inefficiently against transmission. The change in human behaviour is, however, not part of this assessment.
Clinical protection by vaccination has been observed with other vaccines,
but then also seems to reduce transmission [20, 15, 18]. Our simulations show
that reduced transmission in a part of the layers in a flock can reduce exposure
to humans. This might be the reason that vaccination campaigns although with
variable effectiveness [22] in endemic countries can result in less human cases
1
. Vaccination might have played a role, but of course other factors such as
increased awareness, improved bio-security and other control measures could
have played a role.

4.3

Recommendations

To accommodate for uncertainty around the risks of human exposure, the following recommendation can be made based on this modelling study:
• The HI titres dynamics in a real life circumstances during the entire life
cycle of a flock will be found in the current field experiment. With these
new figures this risk assessment should be updated.
• Active surveillance could monitor the occurrence of undetected outbreaks
and the extend of clinical protection in flocks where the virus can spread.
At first such surveillance can determine whether silent spread does occur,
and if this is indeed the case a program can be designed to detect infected
farms within a reasonable time. The results of the current model can be
used to evaluate the benefit of active surveillance. The costs of such a
program can be calculated to evaluate different surveillance strategies on
feasibility and cost-effectiveness.

1 https://www.who.int/publications/m/item/cumulative-number-of-confirmed-humancases-for-avian-influenza-a(h5n1)-reported-to-who–2003-2023-14-july-2023

35

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38

Appendix A

Technical description of the
models
A.1

Overall approach

The modelling approach is two-fold. First we determine the effect of vaccination
on within-farm spread with a stochastic individual-based model for different
production types. This model will be used to determine key-parameters such
as detection time, exposure of humans and probability of a major within-farm
outbreak. These key-parameters are used in the stochastic individual-based
spatial explicit between-farm model in which the farm is the epidemiological
unit.

A.2

Within-farm model

The within-farm models is a two-type stochastic SIR model. The individuals
can move from one type to another type as long as they are susceptible. The
deterministic version of the model is

39

Si
dSi
= − (βii Ii + βji Ij )
− µSi − νij Si + νji Sj
dt
N
dIi
Si
= (βii Ii + βji Ij )
− (µ + γi )Ii
dt
N
dRi
= (1 − ϕi )γi Ii − µi Ri
dt
dDSi
= µSi
dt
dDIi
= (ϕi γi + µ)Ii
dt
dDRi
= µRi
dt

(A.1)
(A.2)
(A.3)
(A.4)
(A.5)
(A.6)

The model describes susceptible animals that are either of one of two types
(subscripts i or j). From next section on-wards, we define two classes high titre
(h) and low titre (l) after vaccination. Transition between these types occurs
at rate νij . Transmission of the infection occurs with transmission parameters
specific for transmitting and receiving animal βij . Infectious birds loose the infection at a type specify rate γi . All animals experience a background mortality
µ, but infectious animals additionally die at recovery with probability ϕi .
In the continuous time Markov chain model (CTMC) the continuous flows
are replaced by stochastic discrete changes in variables with specific rates (Table
A.1) at which these ‘jumps’ occur or probabilities at infection age. The latter
is
Jump
Si → Sj
Si → Ii
Ii → Ri
Si → DSi
Ii → DIi
Ri → DRi



Rate
νij

I

Ii
βii N
+ βji Nj
(1 − ϕi )γ
µ
µ + ϕγ
µ

Table A.1: Transitions of the stochastic model: Either rate or probability at
time at infection age a

Reproduction number R and probability of a minor outbreak
The reproduction number for the model is the average of infections caused by
both types.

40


R=

l
1N
N βll

2



γl

+

Nh
N βhh

γh

v
u
u
+t

Nh
N βhh

γh

−

Nl
N βll

γl



!2
+

l
4 NNh βlh N
N βhl 

γl γh



(A.7)

To estimate the probability of a minor or major outbreak, the CTMC model
is approximated by the Galton–Watson two-type branching process near the
disease-free equilibrium [17]. Specifically the derivation[17] for a model with
differences in host infectivity is used. In short a two-type branching process near
the disease-free equilibrium is a stochastic process that describes the“offspring”
generated by a case in the next time. This model is based on the assumptions
that the number of infecteds is much smaller than the total population size, and
thus depletion of susceptibles can be neglected. Furthermore each ‘branch’ is
considered to be independent.
The probability of a minor outbreak calculated initialized by il and ih birds
with low or high titres [17]:
Pminor = qlil qhih ⇒ Pmajor = 1 − Pminor

(A.8)

The ql and qh are interpreted as the independent probabilities of extinction,
when the infection is introduced by on animal of low or high titre respectively.
These values are obtained by solving the following system:
qh = fh (qh , ql )

(A.9)

ql = fl (qh , ql )

(A.10)

In which fl and fh of offspring probability generating functions (pgf’s) from one
low l or one high titre h animals:
!ah
Nl
h
R
+
(1
−
u
)
R
)
(1 − uh ) NhN+N
hh
l
hl
N
+N
l
h
l
(A.11)
fh (uh , ul ) = 1 +
ah
!al
l
h
Rlh + (1 − ul ) NhN+N
Rll )
(1 − uh ) NhN+N
l
l
fl (uh , ul ) = 1 +
(A.12)
al
(A.13)
This system was solved numerically by function multiroot in R-package
rootSolve.
Outbreak simulations
The model as described in section A.2 (Table A.1) is simulated using R in which
we implemented the Sellke construction [8]. The code of the model can be
found on GitHub (https://github.com/EgilFischer/HPAIVaccination.git). For
each scenario (Table 1.1) the model was run 10 times. Each run represents an
outbreak and was later used to determine the detection time and human exposure. This allows for comparison of different detection methods and parameter
settings for the detection model for the same outbreaks.
41

Detection model
The detection model has two different types of detection methods 1. passive
surveillance and 2. active surveillance. The minimum detection time was determined as the minimum time of either of these two for an outbreak. The active
surveillance model is stochastic and will be run on the same outbreak for several
times. The passive surveillance model is deterministic and will only provide one
detection time per outbreak. Parameters of the detection model can be found
in Table 2.1.
passive surveillance passive surveillance is based on a simple principle of
reaching a specific number of dead birds during a given interval or during subsequent intervals. This includes all dead birds including non-infected or recovered
birds. Here we use the protocol in which a farmer is obliged to report death
above 0.5% of the flock during two consecutive days. The passive surveillance
time will thus be the second day in which the number of deaths is 0.5% of the
flock.
active surveillance active surveillance is based on screening at the end of a
given interval of a certain number of animals with a given test sensitivity. For
each interval the number of dead animals is added, and each infected or recovered
animal has a probability of being sampled and to test positive (sensitivity).
The probability of a farm being detected is the probability of a farm being
inspected multiplied by the probability that at least one animal in the sample
tests positive. This can be done on dead animals or on living animals. Here we
considered the protocol in which dead birds are screened for avian influenza in
all farms at a weekly interval with a per infected bird sensitivity of 0.99 (Table
2.1).

A.2.1

Human exposure

A first approach would be to attempt to quantify the amount of viable virus
particles in the stable, to calculate the number of viable virus particles inhaled
by a human and subsequently calculating the probability of being infected. To
our knowledge only experimental data is available for human adapted influenza
viruses [12, 6]. This approach would, however, introduce several parameters
with high uncertainty. Therefore we approach the matter by comparing the
exposure of humans relative to the baseline based on two simple assumptions:
1. The decrease in virus shedding in high titre birds is completely reflected
by a decrease in transmission rate.
2. The transmission rates of birds to humans is proportionate to the transmission rate of birds to birds
With βii being the transmission rate from type i to animals of the same type
and α a scaling factor for susceptibility if humans to this strain. The exposure
42

of a human being infected at a certain time t is thus:
Z t
βll Yl (τ ) + βhh Yh (τ )
−α
H(t) =
dτ
N
0

(A.14)

The number of infectious birds (Yl and Yh ) are obtained from the simulation
of the stochastic model. From this model we define the course of outbreaks and
the moment of detection based on the number of dead birds in a given interval.
We simulate both unvaccinated and vaccinated situations and report the ratio
of the total exposure until the detection time of an outbreak over the average
of the unvaccinated (baseline) simulations.

A.3

Between-farm model

The between-farm model is an individual based model in which the individual
farm is the epidemiological unit. Each farm has three fixed characteristics: location, size and species. The vaccination status is the fourth characteristic is
drawn for each run of the model.

Infection events
The infection events are determined by the between-farms transmission kernel
(h(rij )) and the probability of a major outbreak on the receiving susceptible
farm based on the vaccination status (πmajor ). The Sellke algorithm enables an
efficient simulation process [2, 8]. For each individual farm a random threshold
is determined, and the farm is infected at the moment that the cumulative
force-of-infection ξ exceeds this threshold. The cumulative force-of-infection is
the force-of-infection exerted at this farm by all infected farms while these are
infectious.
Z tX
ξ(i) = πmajor (i)
Ij (τ )h(rij )dτ
(A.15)
0 j∈J

(
1, if t ≥ t0 & t ≤ t0 + Tj
Ij (t) =
0 otherwise

(A.16)

Infectious period T
The infectious period of a farm is determined by the detection time. We assume
that the infectious period ends at the moment of detection. The moment of detection is determined by the vaccination status as described in the within-farm
model. To obtain an estimate for the distribution of detection time, a gammadistribution was fitted on the results of the within-farm model using R-package
fitdistrplus version 1.1.8.

43

The function between the mean and variance (or standard deviation) of detection time Td are functions of farm size, vaccination status and type of farm
(layer yes/no).
Human exposure
Human exposure per farm is derived from the within-farm model assuming the
full potential of exposure until detection or fade-out. To obtain an estimate
for the distribution of human exposure, a gamma-distribution was fitted on the
results of the within-farm model using R-package fitdistrplus version 1.1.8.
We defined a function for the mean and variance of the distribution for the size,
type and vaccination status of the farm. Detection time was not considered as
a factor because the variation in the human exposure was already determined
(mainly) by these three factors.
The function between the mean and variance (or standard deviation) of human
exposure H were based on farm size, vaccination status and introduction time.
Initialization
Index farms were selected randomly in a high density poultry area (HDPA) or
a low density poultry area (LDPA). DPPA farms were random selected from
those farms with the 5% percentile highest point density within 1 km from a
farm. SPPA were randomly selected among the 75% percentile lowest point
density within 1 km.

A.4

Parameterization

Parameters of the baseline model are given in Table 2.1 and those of the scenarios in Table 1.1.

Farms The size of farms in 2022 were obtained from the Rijksdienst voor
Ondernemend Nederland (RVO) via Wageningen Bioveterinary Research. For
the within-farm scenarios, the 25%-percentile, median and 75%-percentile of
layer and broiler farms were used. The length of a production round (42 days
for broilers and 540 days for layers) and background mortality (0.0005 day−1 )
was obtained by expert elicitation (pers. comm. Dr. Mieke Matthijs).
Transmission The within farm model was parameterized on the experiments
done at WBVR and other literature. In the study by WBVR [9], the average
infectious period was 3 for the control group and 4 for the vaccinated group.
The infectious period was modelled as a gamma distribution with these values
as mean and a rate parameter of 20 [13]. The transmission coefficient of low
titre birds was obtained from [9]. In this study the transmission coefficient of
high titre birds was 0, but using the final size method an upper limit of 0.7

44

of the reproduction number could be obtained. The transmission coefficient
can be calculated by dividing the reproduction number by the infectious period
resulting in 0.175 for the WBVR study [9]. Here we chose to take a lower value
(0.058 day−1 ) obtained from a previous study in which it could be estimated
[21] .
Clinical protection Unvaccinated infected chickens do not survive the infection [9]. For vaccinated chickens 0.1% was expected to die of the infection.
Waning of high titre For the duration of a high titre (Figure A.1, the parameters of a gamma distribution were calibrated on the data of Table 1 of Rudolf
et al. 2010. High titres were titre ≥ 5log2 against challenge strain antigen
(H5N2) and challenge strain antigen (H5N1) after basic immunization. Basic
immunization was vaccination at age 20 weeks and 4 weeks later.

Figure A.1: Duration of high titre. Dots are fraction of vaccinated birds with
high titre ≥ 5 log2 against the heterologous H5N1 strain antigen and the homologous H5N2 strain after basic immunization. Table 1 in Rudolf et al. 2010.
Solid line is probability of having a high titre based on calibrated gamma distribution.

Between farm transmission The between-farm model uses the transmission
kernel for HPAI in the Netherlands from the outbreak of 2003 [4, 2]. The

45

locations, size and type of farms in 2022 were obtained from the Rijksdienst
voor Ondernemend Nederland (RVO) via Wageningen Bioveterinary Research.

46